Your welcome.. systemics will kill every insect for 3-4 months..
I use a systemic from Bayer available at big box stores. A 1/2 teaspoon usually takes care of the infestation and if possible remove all dead or dying plant material.
I have a palm for several years have the same problem in winter . Palm don't like the dry heat causing the plant to dry out . As a result leaves begin to die and insects move in. If you have a place to mist the palm every day , it will keep the plant hydrated enough to stay healthy.
